\(=lim\dfrac{\sqrt{\dfrac{n^2}{n^2}+\dfrac{1}{n^2}}+\dfrac{4n}{n}}{\dfrac{3n}{n}-\dfrac{2}{n}}=lim\dfrac{\sqrt{1+\dfrac{1}{n^2}}+4}{3-\dfrac{2}{n}}=\dfrac{1+4}{3}=\dfrac{5}{3}\)
Tính các giới hạn sau
1,Lim\(\left(\dfrac{2n^3}{2n^2+3}+\dfrac{1-5n^2}{5n+1}\right)\)
2,a,Lim\(\left(\sqrt{n^2+n}-\sqrt{n^2+2}\right)\)
b,Lim\(\dfrac{\sqrt{n^4+3n-2}}{2n^2-n+3}\)
c,Lim\(\dfrac{\sqrt{n^2-4n}-\sqrt{4n^2+1}}{\sqrt{3n^2+1}-n}\)
tính các giới hạn sau:
a) lim (3n2+n2-1)
b)lim \(\dfrac{n^3+3n+1}{2n-n^3}\)
c) lim \(\dfrac{-2n^3+3n+1}{n-n^2}\)
d) lim \(\left(n+\sqrt{n^2-2n}\right)\)
e) lim \(\left(2n-3.2^n+1\right)\)
f) lim \(\left(\sqrt{4n^2-n}-2n\right)\)
g) lim \(\left(\sqrt{n^2+3n-1}-\sqrt[3]{n^3-n}\right)\)
tìm giới hạn:
lim\(\dfrac{5n\sqrt{2n^2-n}}{1+5n-3n^2}\)
lim\(\dfrac{\sqrt{4n^2+n}-7n}{3n^2-1}\)
có bao nhiêu giá trị nguyên a để \(lim\dfrac{\sqrt{an^3+n^2+1}-n\sqrt{2n+1}}{\sqrt{4n^3+3n}}\le\sqrt{2}\)
Tìm các giới hạn sau:
a) \(lim\dfrac{5n}{n-\sqrt{n^2-n-1}}\)
b) \(lim\dfrac{\sqrt{n+\sqrt{n+1}}}{n-\sqrt{n}}\)
c) \(lim\dfrac{\sqrt{2n^4-n^2+7}}{3n+5}\)
d) \(lim\dfrac{\sqrt{3n^2+2n}-n}{3n-2}\)
Tìm các giới hạn sau :
a) \(\lim\limits\dfrac{6n-1}{3n+2}\)
b) \(\lim\limits\dfrac{3n^2+n-5}{2n^2+1}\)
c) \(\lim\limits\dfrac{3^n+5.4^n}{4^n+2^n}\)
d) \(\lim\limits\dfrac{\sqrt{9n^2-n+1}}{4n-2}\)
Tìm các giới hạn sau:
a) \(lim\sqrt[3]{-n^3+2n^2-5}\)
b) \(lim\dfrac{1}{\sqrt{n+1}-\sqrt{n}}\)
c) \(lim\left(\dfrac{1}{n+1}-n\right)\)
d) \(lim\left(\dfrac{2n^2-1}{n+1}-2n\right)\)
e) \(lim\dfrac{2n^3+n^2-3n+1}{2-3n}\)
đặt \(a=lim\dfrac{3n^3-2n+1}{4n^4+2n+1}\). tìm \(lim\dfrac{an^3-\left(a+2\right)n^2+1}{4an^3-n^2+3n+3}\)
Tính các giới hạn sau:
\(lim\sqrt{n}\left(\sqrt{n+1}-n\right)\)
\(lim\dfrac{\sqrt{4n^2+1}+2n-1}{\sqrt{n^2+4n+1}+n}\)
